connecting theme to website before moving the domain

I currently have my website hosted and I intend to move this website during the upcomming weeks. However I wish to rebuild the site and have this dine before I transfer the domain.
The problem is from what I could understand that the theme I wish to use is in this case "fundamental" and upon purchase it is to be connected to the domain.
Is there a way that I can purchase the theme and start to work on the new website and when I am finished transfer the domain to my new host ?
Basicly i wish to use the old site until the new one is done with no "downtime" but the theme connected to domain gives me a problem.

Thanks in advance for any help that can explain how to solve this issue for me.